The notion of balanced pairs involving two additive full subcategories
of an abelian category \(\mathcal {A}\)  was introduced by Chen [1]}, which generalizes projectives and injectives from homological aspects. In
general, a balanced pair always shares many similar properties with the projectives and injectives. We refer to Chen [1]} for more details. It should be noted that this subject first appeared in Enochs' work (see [3]} for instance), where a pair \((\mathcal {H}, \mathcal {G})\)  in \(\mathcal {A}\)  is balanced if
and only if the bifunctor \(\textrm {Hom}_{\mathcal {A}}(-,-)\)  is right balanced by \(\mathcal {H}\times \mathcal {G}\) . For examples of balanced pairs, the reader may refer to [3]}. An interesting and deep
result in [5]} is that in an abelian category \(\mathcal {A}\)  with small Ext groups, there
exists a one-to-one correspondence between balanced pairs and Quillen exact structures \(\xi \)  with enough \(\xi \) -projectives and enough \(\xi \) -injectives. Motivated by this, it seems natural to introduce the notion of balanced pairs in a triangulated category \(\mathcal {C}\) , and to establish certain relations connecting balanced pairs with certain classes of triangles in \(\mathcal {C}\) . Thus, we have the following main result of this paper.
